Question 1

Why is a 20% rise then a 20% fall not break-even?

Accepted Answer

Because the second percentage is taken from a bigger number. The 20% you added was 20 of 100; the 20% you removed was 24 of 120. This is also why an investment that drops 50% needs a 100% gain to recover.

Question 2

What is the difference between percent and percentage points?

Accepted Answer

If a rate goes from 4% to 5%, that is a rise of one percentage point, but a 25% increase. Financial reporting mixes these up constantly, usually in whichever direction sounds better.